Geodesic
Chief Factor Sizes in Finitely Generated Varieties
Canadian journal of mathematics, Tome 54 (2002) no. 4, pp. 736-756

Voir la notice de l'article provenant de la source Cambridge University Press

Let $\mathbf{A}$ be a $k$ -element algebra whose chief factor size is $c$ . We show that if $\mathbf{B}$ is in the variety generated by $\mathbf{A}$ , then any abelian chief factor of $\mathbf{B}$ that is not strongly abelian has size at most ${{c}^{k-1}}$ . This solves Problem 5 of The Structure of Finite Algebras, by D. Hobby and R. McKenzie. We refine this bound to $c$ in the situation where the variety generated by $\mathbf{A}$ omits type 1. As a generalization, we bound the size of multitraces of types 1, 2, and 3 by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity.
DOI : 10.4153/CJM-2002-028-x
Mots-clés : 08B26, tame congruence theory, chief factor, multitrace 
Kearnes, K. A.; Kiss, E. W.; Szendrei, Á.; Willard, R. D. Chief Factor Sizes in Finitely Generated Varieties. Canadian journal of mathematics, Tome 54 (2002) no. 4, pp. 736-756. doi: 10.4153/CJM-2002-028-x
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